The sampling variance of the correlation coefficients estimated from two-fold nested and offspring-parent regression analyses.

A formula is presented for the large-sample variance of phenotypic, genetic and environmental correlation coefficients, estimated from two-fold nested genetic analyses of balanced or unbalanced offspring data. Where parents of these offspring are scored, offspring on parent regression estimates of genetic parameters may be obtained for each parental level of the nested model. The large-sample variance of the offspring-parent genetic correlation coefficients, computed from either level or by using mid-parent data, is given. The first formula is a correction and generalisation of an expression given by Grossman (1970), while the second formula is an extension of a relationship derived by Reeve (1955).